Re: Exclusive Disjunction vs False Dilemma

From: Immortalist (Reanimater_2000_at_yahoo.com)
Date: 08/29/04 

Date: Sun, 29 Aug 2004 09:51:39 -0700

"ZZBunker" <zzbunker@netscape.net> wrote in message
news:e4a0829b.0408290537.5a009252@posting.google.com...
> "Immortalist" <Reanimater_2000@yahoo.com> wrote in message
news:<HbOdnZwfYaOp9Y3cRVn-jA@comcast.com>...
> > In logic, a disjunction is a compound sentence formed by combining two
sentences
> > (or facts) using the word "or."
> >
> > A disjunction is true when EITHER or BOTH sentences (or facts) are true.
> >
> > Examples:
> >
> > 1. "Blue is a color or 7 + 3 = 10."
> >
> > (T or T = T) Since both facts are true, the entire sentence is true.
> >
> > 2. "One hour = exactly 55 minutes or one minute = exactly 60 seconds."
> >
> > (F or T = T) Since the second fact is true, the entire sentence is true.
> >
> > 3. "3 + 4 = 6 or all dogs meow."
> >
> > (F or F = F) Since both facts are false, the entire sentence is false.
> >
> > 4. "The word cat has 3 letters or the word dog has four letters."
> >
> > (T or F = T) Since the first fact is true, the entire sentence is true.
> >
> > http://regentsprep.org/Regents/math/tables/disjunct.htm
> >
> > ----------------------------------------------
> >
> > "Tim" <arg@rag.dsj> wrote in message
> > news:wZWdnVdodfYdt43cRVn-vQ@edaptivity.com...
> > >
> > > "HVAC" <victorallencampbell@hotmail.com> wrote in message
> > > news:9757f47e.0408031006.295b65ed@posting.google.com...
> >
> > > > .......The only voice of reason here?
> > > >
> > > > I mean, I read these fucking kooks and sometimes
> > > > I wonder if they could possibly hold down a job?
> > > >
> > > > The answer is scary either way.
> > > >
> > > > 1) These fucking morons DON'T have a job and I'm supporting
> > > > their tired asses.
> > > >
> > > > Or
> > > >
> > > > 2) They DO have jobs and I just have to hope that their
> > > > not important because they can't figure out jack ***.
> > > >
> > > > Think about it...Would you want Twonky anywhere near you?
> > >
> > > What type of people did you expect to find at
> > > alt.alien.research,alt.alien.visitors,alt.paranormal.crop-circles?
> > > Not to say the alt.philosophy crowd is outstanding in any way
> > > shape or form. As to your idea about you being the voice of reason
> > > I'll point out that your disjunction is not valid. Maybe you
> > > should keep your voice to a whisper.
> > >
> >
> > If the first part of the disjunct is an unknown or has no justificatory
arguments
> > for its falsity then the second part of the disjunct implies a necessary
> > connection that shows the first part to be false if it, the second part, is
true.
> >
> > Alternatively if the first part of the conjunction has no known justification
for
> > its falsity and it doesn't depend upon the second conjunct as grounds for
truth
> > or falsity then it begs the question.
> >
> > Finally there must be an argument to show the truth or falsity of each
conjunct
> > on its own in order to match propositional calculus mathematics. Hence a
logical
> > disjunction transforms to an exclusive dijunction if there is no evidence or
> > argument for the truth or falsity of either disjunct and thus becomes
contingent
> > upon the truth condition of the opposing side?
> >
> > Exclusive disjunction
> >
> > In logic, exclusive disjunction is a logical operator. The exclusive
disjunction
> > of propositions A and B is usually called A xor B, where "xor" stands for
> > "exclusive or" and is pronounced "ex-or".
> >
> > The operation yields the result TRUE when one, and only one, of its operands
is
> > TRUE.
> >
> > For two inputs A and B, the truth table of the function is as follows.
> >
> > A B | A xor B
> > ----+--------
> > F F | F
> > F T | T
> > T F | T
> > T T | F
> >
> > It can be deduced from this table that
> >
> > (A xor B) = (A and not B) or (not A and B) = (A or B) and (not A or not B) =
(A
> > or B) and not (A and B)
> >
> > The mathematical symbol for exclusive disjunction varies in the literature.
In
> > addition to the abbreviation "xor", one may see
> >
> > * a plus sign ("+") or a plus sign that is modified in some way, such as
being
> > put inside a circle ("?"); this is used because exclusive disjunction
corresponds
> > to addition modulo 2 if F = 0 and T = 1.
> >
> > * a vee that is modified in some way, such as being underlined ("?"); this is
> > used because exclusive disjunction is a modification of ordinary (inclusive)
> > disjunction, which is typically denoted by a vee.
> >
> > * a caret ("^"), as in the C programming language
> >
> > Similarly, different textual notations are used, including "EOR" (with the
same
> > expansion as "xor") and "orr" (modelled on iff, of which it is the negative).
> >
> > Binary values xor'ed by themselves are always zero. In some computer
> > architectures, it is faster to store a zero in a register by xor'ing the
value
> > with itself instead of loading and storing the value zero. Thus, on some
computer
> > architectures, xor'ing values with themselves is a common optimization.
> >
> > The xor operation is sometimes used as a simple mixing function in
cryptography,
> > for example, with one-time pad or Feistel network systems.
> >
> > http://www.fact-index.com/e/ex/exclusive_disjunction.html
> > http://www.fact-index.com/l/lo/logical_disjunction.html
> >
> > -----------------------------------------
> >
> That's not true though. Since one of the main points
> of Cantor's theorem is to show that XOR is
> a fallacy of mathematics, not logic.
>
> Since it's really impossible for there to be anything
> true or false about XOR, since it's not really
> used by cryptographers, it was invented by cryptographers.
>

I use it when I desire to make a distinction between AND/OR and EITHER/OR.

>
>
> > False Dilemma
>
> False Dilemma itself it totally fallacious reasoning,
> and the source of the error. Since Senatorial
> statements aren't examples of false dilemma,
> given that Senators invented false dilemma,
> with their Logic-101 failure to understand
> that a context is not a dilemma, it's a quandary.
>

Either 1+1=4 or 1+1=12.

1+1=4 is false therefore 1+1=12 is true?

>
> > A False Dilemma is a fallacy in which a person uses the following pattern of
> > "reasoning":
> >
> > 1. Either claim X is true or claim Y is true (when X and Y could both be
> > false).
> >
> > 2. Claim Y is false.
> >
> > 3. Therefore claim X is true.
> >
> > This line of "reasoning" is fallacious because if both claims could be false,
> > then it cannot be inferred that one is true because the other is false. That
this
> > is the case is made clear by the following example:
> >
> > 1. Either 1+1=4 or 1+1=12.
> >
> > 2. It is not the case that 1+1=4.
> >
> > 3. Therefore 1+1=12.
> >

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